Connection between even and odd numbers and functions | Algebra II | Khan Academy

TL;DR

Even functions and odd functions have a clear connection to even and odd numbers, with exponents in simple polynomial functions determining whether the function is even or odd.

Transcript

In the last video on even and odd functions, I talk about how you shouldn't get confused between even functions and even numbers and odd functions and odd numbers. And I said that there wasn't any obvious connection between the word even function and our notion of even numbers, or any connection between odd functions and odd numbers. And, I was wro... Read More

Key Insights

• 🦕 There is a clear connection between even functions and even numbers, and odd functions and odd numbers.
• 🦕 Exponents in simple polynomial functions determine whether a function is even or odd.
• 🦕 Not all even or odd functions have exponents, but the motivations for naming them as such likely come from the archetypal examples with exponents.

Questions & Answers

Q: How are even functions and odd functions connected to even and odd numbers?

Even functions and odd functions are connected to even and odd numbers through the presence of exponents in simple polynomial functions. The exponent determines whether the function is even or odd.

Q: Do all even or odd functions have exponents?

No, not all even or odd functions have exponents. They can be trigonometric functions or other types of functions. However, the presence of exponents in simple polynomial functions likely motivated the naming of even and odd functions.

Q: Are all functions with exponents considered even or odd?

No, not all functions with exponents are considered even or odd. The motivation for naming a function as even or odd stems from the presence of exponents in simple polynomial functions, not all functions.

Q: Can functions with other terms be considered even or odd?

Functions with other terms beyond the pure "x" raised to a power cannot be easily classified as even or odd. Only when a function is stripped down to a simple polynomial expression, such as "x^3" or "x," can it be classified as odd or even.

Summary & Key Takeaways

• The video explains that there is a connection between even functions and even numbers, and odd functions and odd numbers, despite the initial belief that there was no connection.

• The connection is evident in simple polynomial functions where the exponent of "x" determines whether the function is even or odd.

• Not all even or odd functions have exponents, but the motivations for naming them even or odd likely come from the presence of exponents in archetypal examples.